Mixture probability distribution functions to model wind speed distributions

International Journal of Energy and Environmental Engineering Mixture probability distribution functions to model wind speed distributions Ravindra Kollu 0 Srinivasa Rao Rayapudi 0 SVL Narasimham 1 Krishna Mohan Pakkurthi 0 0 Department of Electrical and Electronics Engineering, J.N.T. University Kakinada , Kakinada, Andhra Pradesh 533003, INDIA 1 Computer Science and Engineering Department, School of Information Technology, J.N.T. University Hyderabad , Hyderabad, Andhra Pradesh 500085, INDIA Accurate wind speed modeling is critical in estimating wind energy potential for harnessing wind power effectively. The quality of wind speed assessment depends on the capability of chosen probability density function (PDF) to describe the measured wind speed frequency distribution. The objective of this study is to describe (model) wind speed characteristics using three mixture probability density functions Weibull-extreme value distribution (GEV), Weibull-lognormal, and GEV-lognormal which were not tried before. Statistical parameters such as maximum error in the Kolmogorov-Smirnov test, root mean square error, Chi-square error, coefficient of determination, and power density error are considered as judgment criteria to assess the fitness of the probability density functions. Results indicate that Weibull-GEV PDF is able to describe unimodal as well as bimodal wind distributions accurately whereas GEV-lognormal PDF is able to describe familiar bell-shaped unimodal distribution well. Results show that mixture probability functions are better alternatives to conventional Weibull, two-component mixture Weibull, gamma, and lognormal PDFs to describe wind speed characteristics. Mixture distributions; Probability density functions; Wind speed distribution - Background Growing global population along with fast depleting reserves of fossil fuels is influencing researchers to search for clean and pollution-free sources of energy such as solar, wind, and bioenergies. Wind energy is a never ending natural resource which has shown its great potential in combating climate change while ensuring clean and efficient energy. Further, rapid advances in wind turbine technology led to significant growth of wind power generation across the world. However, wind energy is more sensitive to variations with topography and wind patterns compared to solar energy. Wind energy can be harvested economically if the turbines are installed in a windy area and suitable turbine is properly selected. Wind speed forecasting is a critical factor in assessing wind energy potential and performance of wind energy conversion systems. Several probability density functions (PDFs) have been used in literature to describe wind speed characteristics which include Weibull, Rayleigh, bimodal Weibull, lognormal, gamma, etc. Islam et al. [1] used two-parameter Weibull distribution function for wind speed forecasting and assessed wind energy potentiality at Kudat and Labuan, Malaysia. Celik [2] used Weibull-representative wind data instead of the measured data in time-series format for estimating the wind energy and had shown that estimated wind energy is highly accurately. Celik [3] made statistical analysis of wind data at southern region of Turkey and summarized that Weibull model was better than Rayleigh model in fitting the measured data distributions. Akdag et al. [4] discussed the suitability of two-parameter Weibull wind speed distribution and the two-component mixture Weibull distribution (WW-PDF) to estimate wind speed characteristics. Carta et al. [5] used WW-PDF because it is able to represent heterogeneous wind regimes in which there was evidence of bimodality or bitangentiality or, simply, unimodality. Maximum likelihood and least-square methods were used to estimate WW-PDF parameters. In [6], wind speed distributions were shown to be satisfactorily described with a log-normal function, and in [7], Weibull and lognormal distribution functions were used to fit wind speed distributions. Kiss and Imre [8] used Rayleigh, Weibull, and gamma distributions to model wind speeds both over land and sea. They found that generalized gamma distribution, which has independent shape parameters for both tails, provides an adequate and unified description almost everywhere. Generalized extreme value (GEV) distribution that combines the Gumbel, Frechet, and Weibull extreme value distributions were used to model extreme wind speeds [9-12]. In recent past, mixture distributions were used to estimate wind energy potential that are quite accurate in describing wind speed characteristics. Jaramillo and Borja [13] used mixture Weibull distribution (WW) to model bimodal wind speed frequency distribution. Akpinar et al. [14] used mixture normal and Weibull distribution (NW), which is a mixture of truncated normal distribution, and conventional Weibull distribution to model wind speeds. Tian Pau [15] employed mixture gamma and Weibull distribution (GW) which is a combination of gamma and Weibull distributions, and also mixture normal distribution (NN) which is a mixture function of two-component truncated normal distribution for wind speed modeling. The objective of this study is to propose three new mixture distributions, viz., Weibull-lognormal (WL), GEV-lognormal (GEVL), and Weibull-GEV (WGEV) for wind speed forecasting. Comparison of the proposed mixture distributions with existing distribution functions is done to demonstrate their suitability in describing wind speed characteristics. The rest of this paper is organized as follows: wind distribution models and goodness of fit tests used in this paper are presented in the section Methods. Results derived from this study are discussed in Results and discussions section. Details about the data used for the analysis are given in this section. Conclusions are presented in the Conclusions section. Methods Significance The most suitable wind turbine model which needs to be installed in a wind farm is selected by careful wind energy resource evaluation. Accurate evaluation could be done using best fit distribution model. Using inappropriate distribution models results in inaccurate estimation of wind turbine capacity factor and annual energy production which in turn leads to improper estimation of levelized production cost [13]. Hence, it is important to choose an accurate distribution model which closely mimics the wind speed distribution at a particular site. Wind distribution models Wind distribution modeling requires analysis of wind data over a number of years. To reduce the expenses and time required to process long-term wind speed data, it is desirable to use statistical distribution functions for describing the wind speed variations. The primary tools to describe wind speed characteristics are probability density functions. The parameters of probability distribution functions which describe wind-speed frequency distribution are estimated using statistical data of a few years. (...truncated)